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Abelian maximal pattern complexity of words

  • TETURO KAMAE (a1), STEVEN WIDMER (a2) and LUCA Q. ZAMBONI (a3) (a4)


In this paper, we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection. We show that in the case of binary words, the bound is actually achieved and gives a characterization of recurrent aperiodic words.



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[1]Coven, E. M. and Hedlund, G. A.. Sequences with minimal block growth. Math. Syst. Theory 7 (1973), 138153.
[2]McCutcheon, R.. Elementary Methods in Ergodic Ramsey Theory (Lecture Notes in Mathematics, 1722). Springer, Berlin, 1999 (in Ch. 2).
[3]Kamae, T. and Zamboni, L. Q.. Sequence entropy and the maximal pattern complexity of infinite words. Ergod. Th. & Dynam. Sys. 22 (2002), 11911199.
[4]Kamae, T. and Rao, H.. Maximal pattern complexity over $\ell $ letters. European J. Combin. 27 (2006), 125137.
[5]Kamae, T.. Uniform sets and super-stationary sets over general alphabets. Ergod. Th. & Dynam. Sys. 31 (2011), 14451461.
[6]Morse, M. and Hedlund, G. A.. Symbolic dynamics II: Sturmian trajectories. Amer. J. Math. 62 (1) (1940), 142.
[7]Richomme, G., Saari, K. and Zamboni, L. Q.. Abelian complexity of minimal subshifts. J. Lond. Math. Soc. (2) 83 (2011), 7995.


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